A splash plate reflector antenna is characterized by a flat, planar metal surface that reflects power radiated from a waveguide, or feed tube, to a main reflector. Such an antenna employing a corrugated splash plate is sometimes referred to as a "Hat Feed" antenna. The present invention builds upon the hat feed antenna seen in U.S. Pat. No. 4,963,878 to Per-Simon Kildal. The goal of the Kildal hat feed design was to produce equal E- and H-plane patterns. It was later observed in the paper by J. P. Hansen, A. A. Kishk, P. S. Kildal and O. Dahlsjo entitled "High Performance Reflector Hat Antenna With Very Low Sidelobes For Radio Link Applications," Antenna and Propagation Symposium Proceedings, July 1995, Newport Beach, Calif., that Kildal's feed could be used for low sidelobe antenna design. This is because the feed has a very smooth primary pattern and low sidelobes. Our invention builds upon this design. It uses a main reflector that subtends a large portion of the feed pattern (approximately 110 degrees). The feed pattern has a large edge taper on the reflector (-20 db) that in turn gives a very low sidelobe radiation pattern without use of an absorbing cylinder. In place of the splash plate, a subreflector which is tapered rather than flat and having varied depth of its corrugations helps guide the energy from the feed to the main reflector along a path which insures improved low sidelobes. The feed geometry is much smaller than that described in the above patent and thus has less subreflector blockage. Further the feed tube is much shorter.